Problem: ${\sqrt[3]{81} = \text{?}}$
$\sqrt[3]{81}$ is the number that, when multiplied by itself three times, equals $81$ First break down $81$ into its prime factorization and look for factors that appear three times. So the prime factorization of $81$ is $3\times 3\times 3\times 3$ Notice that we can rearrange the factors like so: $81 = 3 \times 3 \times 3 \times 3 = (3\times 3\times 3) \times 3$ So $\sqrt[3]{81} = \sqrt[3]{3\times 3\times 3} \times \sqrt[3]{3}$ $\sqrt[3]{81} = 3 \sqrt[3]{3}$